The dynamics of the risk perception on a social network and its effect on disease dynamics

The perceived infection risk changes individual behaviors, which further affects the disease dynamics. This perception is influenced by social communication, including surveying their social network neighbors about the fraction of infected neighbors and averaging their neighbors' perception of the risk. We model the interaction of disease dynamics and risk perception on a two-layer random network that combines a social network layer with a contact network layer. We found that if information spreads much faster than disease, then all individuals converge on the true prevalence of the disease. On the other hand, if the two dynamics have comparable speeds, the risk perception still converges to a value uniformly on the network. However, the perception lags behind the true prevalence and has a lower peak value. We also study the behavior change caused by the perception of infection risk. This behavior change may affect the disease dynamics by reducing the transmission rate along the edges of the contact network or by breaking edges and isolating the infectious individuals. The effects on the basic reproduction number, the peak size, and the final size are studied. We found that these two effects give the same basic reproduction number. We find edge-breaking has a larger effect on reducing the final size, while reducing the transmission rate has a larger effect on reducing the peak size, which is true for both scale-free and Poisson networks.